Chords AB and CD meet at point E. Find CD if AE = 4cm, BE = 9cm, and CE is four times the length of DE.

By the property of intersecting chords of a circle, the product of the segments of one chord formed by the intersection point is equal to the product of the segments of the other chord.

Let the length of the segment DE be equal to X cm, then, by condition, the length of the segment CE = 4 * X cm.

EA * EB = EC * ED.

4 * 9 = 4 * X * X.

4 * X ^ 2 = 36.

X ^ 2 = 9.

X = DE = 3 cm.

CE = 4 * 3 = 12 cm.

Determine the length of the segment CD.

CD = CE + DE = 12 + 3 = 15 cm.

Answer: The length of the CD segment is 15 cm.